Containers for shipping nuclear, radioactive, and/or other hazardous material can have a dual structure, whereby an inner container storing the hazardous material is encapsulated within an outer container to protect the inner container. In one type of shipping container assembly, a 30-gallon drum-type vessel can be encased within a 55-gallon drum-type vessel. Both vessels can include a barrel-like body closed by a lid. The 55-gallon drum-type vessel can include a filling or insulation, such as cardboard or fiberboard, around the 30-gallon drum-type vessel.